Question

How many different straight lines can be formed by joining 14 different points of which 6 are collinear and rest are non-collinear?

• A. 76
• B. 63
• C. 64
• D. 77

Answer 1

The correct option is D 77

No. of lines formed by joining 14 points =${}^{14}{C}_2$

No. of lines formed by joining 6 points =${}^6{C}_2$

Out of the 14 points, when you join the 6 collinear points, you don’t get${}^6{C}_2$lines, but you get only one line.

So, no. of lines${=}^{14}{C}_2{-}^6{C}_2+1=91-15+1=77$.

2nd method:- By selection, ${}^8{C}_2{+}^8{C}_1{\times }^6{C}_1+1=77$ .